Boundary Blow-Up Solutions of Cooperative Systems
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 5, p. 1767-1791
@article{AIHPC_2009__26_5_1767_0,
author = {D\'aVila, Juan and Dupaigne, Louis and Goubet, Olivier and Mart\'\i Nez, Salom\'e},
title = {Boundary Blow-Up Solutions of Cooperative Systems},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {26},
number = {5},
year = {2009},
pages = {1767-1791},
doi = {10.1016/j.anihpc.2008.12.003},
zbl = {1175.35045},
mrnumber = {2566709},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2009__26_5_1767_0}
}

DáVila, Juan; Dupaigne, Louis; Goubet, Olivier; MartíNez, Salomé. Boundary Blow-Up Solutions of Cooperative Systems. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 5, pp. 1767-1791. doi : 10.1016/j.anihpc.2008.12.003. http://www.numdam.org/item/AIHPC_2009__26_5_1767_0/

[1] Bandle C., Asymptotic Behavior of Large Solutions of Elliptic Equations, An. Univ. Craiova Ser. Mat. Inform. 32 (2005) 1-8. | MR 2215890 | Zbl 1120.35014

[2] Bandle C., Marcus M., Asymptotic Behaviour of Solutions and Their Derivatives, for Semilinear Elliptic Problems With Blowup on the Boundary, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995) 155-171. | Numdam | MR 1326666 | Zbl 0840.35033

[3] Bandle C., Marcus M., Large Solutions of Semilinear Elliptic Equations: Existence, Uniqueness and Asymptotic Behaviour, J. Anal. Math. 58 (1992) 9-24. | MR 1226934 | Zbl 0802.35038

[4] Chuaqui M., Cortazar C., Elgueta M., Garcia-Melian J., Uniqueness and Boundary Behavior of Large Solutions to Elliptic Problems With Singular Weights, Comm. Pure Appl. Anal. 3 (4) (2004) 653-662. | MR 2106305 | Zbl 1174.35386

[5] Dancer E. N., Du Y., Effects of Certain Degeneracies in the Predator-Prey Model, SIAM J. Math. Anal. 34 (2) (2002) 292-314. | MR 1951776 | Zbl 1055.35046

[6] Díaz J. I., Lazzo M., Schmidt P. G., Large Solutions for a System of Elliptic Equations Arising From Fluid Dynamics, SIAM J. Math. Anal. 37 (2) (2005) 490-513. | MR 2176113 | Zbl 1136.35360

[7] Du Y., Effects of a Degeneracy in the Competition Model. I. Classical and Generalized Steady-State Solutions, J. Differential Equations 181 (1) (2002) 92-132. | MR 1900462 | Zbl 1042.35016

[8] Du Y., Effects of a Degeneracy in the Competition Model. II. Perturbation and Dynamical Behaviour, J. Differential Equations 181 (1) (2002) 133-164. | MR 1900463 | Zbl 1042.35017

[9] Dumont S., Dupaigne L., Goubet O., Radulescu V., Back to the Keller-Osserman Condition for Boundary Blow-Up Solutions, Adv. Nonlinear Stud. 7 (2007) 271-298. | MR 2308040 | Zbl 1137.35030

[10] García-Melián J., Sabina De Lis J., Letelier-Albornoz R., The Solvability of an Elliptic System Under a Singular Boundary Condition, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 509-546. | MR 2227806 | Zbl pre05054124

[11] García-Melián J., Rossi J. D., Boundary Blow-Up Solutions to Elliptic Systems of Competitive Type, J. Differential Equations 206 (2004) 156-181. | MR 2093922 | Zbl 1162.35359

[12] García-Melián J., Suárez A., Existence and Uniqueness of Positive Large Solutions to Some Cooperative Systems, Adv. Nonlinear Stud. 3 (2003) 193-206. | MR 1971311 | Zbl 1045.35025

[13] Gilbarg D., Trudinger N.-S., Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224, second ed., Springer-Verlag, Berlin, 1983. | MR 737190 | Zbl 0562.35001

[14] Kato T., Schrödinger Operators With Singular Potentials, Israel J. Math. 13 (1972) 135-148. | MR 333833 | Zbl 0246.35025

[15] Keller J., On Solutions to $\Delta u=f\left(u\right)$, Comm. Pure Appl. Math. 10 (1957) 503-510. | MR 91407 | Zbl 0090.31801

[16] López-Gómez J., Coexistence and Meta-Coexistence for Competing Species, Houston J. Math. 29 (2) (2003) 483-536. | MR 1987588 | Zbl 1034.35062

[17] Osserman R., On the Inequality $\Delta u\ge f\left(u\right)$, Pacific J. Math. 7 (1957) 1641-1647. | MR 98239 | Zbl 0083.09402

[18] Pao C. V., Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. | MR 1212084 | Zbl 0777.35001

[19] Protter M., Weinberger H., Maximum Principles in Differential Equations, corrected reprint of the 1967 original, Springer-Verlag, New York, 1984. | MR 762825 | Zbl 0549.35002